Lattice Boltzmann model for the one-dimensional nonlinear Dirac equation

2009 ◽  
Vol 79 (6) ◽  
Author(s):  
Baochang Shi ◽  
Zhaoli Guo
Keyword(s):  
Dirac Equation ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
One Dimensional ◽  
Nonlinear Dirac Equation ◽  
The One ◽  
Boltzmann Model

ONE-DIMENSIONAL QUANTUM LATTICE BOLTZMANN SCHEME FOR THE NONLINEAR DIRAC EQUATION

2013 ◽  
Vol 24 (12) ◽  
pp. 1340001 ◽  
Author(s):  
SILVIA PALPACELLI ◽  
PAUL ROMATSCHKE ◽  
SAURO SUCCI
Keyword(s):  
Dirac Equation ◽  
Lattice Boltzmann ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Quantum Lattice ◽  
One Dimensional ◽  
Dynamic Mass ◽  
Nonlinear Dirac Equation ◽  
Njl Model ◽  
Lattice Boltzmann Scheme

We develop a quantum lattice Boltzmann (QLB) scheme for the Dirac equation with a nonlinear fermion interaction provided by the Nambu–Jona-Lasinio (NJL) model. Numerical simulations in 1 + 1 space-time dimensions, provide evidence of dynamic mass generation, through spontaneous breaking of chiral symmetry.

DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS

2012 ◽  
Vol 19 ◽  
pp. 90-99
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
JINSHENG CAI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
One Dimensional ◽  
Volume Method ◽  
Boltzmann Method ◽  
Boltzmann Model

In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

Scattering operator for the one-dimensional Dirac equation with power nonlinearity

2016 ◽  
Vol 13 (04) ◽  
pp. 821-832
Author(s):  
Nakao Hayashi ◽  
Hironobu Sasaki
Keyword(s):  
Dirac Equation ◽  
Sobolev Space ◽  
Weighted Sobolev Space ◽  
Scattering Operator ◽  
One Dimensional ◽  
Power Nonlinearity ◽  
Nonlinear Dirac Equation ◽  
The One

We consider the nonlinear Dirac equation with a power nonlinearity [Formula: see text] where [Formula: see text], [Formula: see text]. We prove the existence of the scattering operator in the neighborhood of the origin of the weighted Sobolev space [Formula: see text], where [Formula: see text].

MESOSCOPIC SPECTRA IN TWO-DIMENSIONAL DECAYING TURBULENCE

2006 ◽  
Vol 17 (04) ◽  
pp. 531-543 ◽  
Author(s):  
GÁBOR HÁZI
Keyword(s):  
Lattice Boltzmann ◽  
Particle Distribution ◽  
Power Spectra ◽  
Collision Operator ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Two Dimensional ◽  
Decaying Turbulence ◽  
The One ◽  
Boltzmann Model

Two-dimensional decaying turbulence is simulated using a lattice Boltzmann model with the Bhatnagar–Gross–Krook collision operator. Auto-power spectra of the one-velocity particle distribution functions are presented. The relation between the spectrum of the kinetic energy and the spectra of the distribution functions is given. An interpretation of the non-equilibrium spectra as a measure of the dissipation in different scales is given. A peak in the spectrum of the resting particle distribution functions is observed exactly at the ultraviolet cutoff. It is shown that the peak can be associated with enhanced acoustic activity, which might be a numerical artifact or a consequence of the compressibility of the lattice Boltzmann fluid.

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

2012 ◽  
Vol 4 (04) ◽  
pp. 454-472 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Free Parameter ◽  
Compressible Flows ◽  
Computation Time ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Test Problems ◽  
One Dimensional ◽  
Application Range ◽  
Boltzmann Model

AbstractThis paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.

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